A Basis Theory Primer Expanded Edition /

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. T...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Heil, Christopher (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2011.
Edition:1st ed. 2011.
Series:Applied and Numerical Harmonic Analysis,
Subjects:
Harmonic analysis.
Engineering mathematics.
Engineering-Data processing.
Functional analysis.
Fourier analysis.
Mathematics.
Signal processing.
Abstract Harmonic Analysis.
Mathematical and Computational Engineering Applications.
Functional Analysis.
Fourier Analysis.
Applications of Mathematics.
Signal, Speech and Image Processing .
Online Access:Texto Completo
Table of Contents:
  • ANHA Series Preface
  • Preface
  • General Notation
  • Part I. A Primer on Functional Analysis
  • Banach Spaces and Operator Theory
  • Functional Analysis
  • Part II. Bases and Frames
  • Unconditional Convergence of Series in Banach and Hilbert Spaces
  • Bases in Banach Spaces
  • Biorthogonality, Minimality, and More About Bases
  • Unconditional Bases in Banach Spaces
  • Bessel Sequences and Bases in Hilbert Spaces
  • Frames in Hilbert Spaces
  • Part III. Bases and Frames in Applied Harmonic Analysis
  • The Fourier Transform on the Real Line
  • Sampling, Weighted Exponentials, and Translations
  • Gabor Bases and Frames
  • Wavelet Bases and Frames
  • Part IV. Fourier Series
  • Fourier Series
  • Basic Properties of Fourier Series
  • Part V. Appendices
  • Lebesgue Measure and Integration
  • Compact and Hilbert-Schmidt Operators
  • Hints for Exercises
  • Index of Symbols
  • References
  • Index.

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